((3x/(2x-1))+8) Is this a Polynomial

[Maddy_Math]

Hi buddies please help me sort out

" ((3x/(2x-1))+8) Is this a Polynomial " I can't factor it out please help

 

[Deleted member 4993]

Hi buddies please help me sort out

" ((3x/(2x-1))+8) Is this a Polynomial " I can't factor it out please help

What is the definition of polynomial?

 

[Maddy_Math]

What is the definition of polynomial?

I read it as

P(x) = a x^n + b x^n-1 + c x^n-2 + ...........+ z x^n-n
but main problem here is to first simplify the expression

 

[lookagain]

I read it as

P(x) = a x^n + b x^(n-1) + c x^(n-2) + ...........+ z x^(n-n)

You must have grouping symbols around those certain exponents.

 

[JeffM]

Hi buddies please help me sort out

" ((3x/(2x-1))+8) Is this a Polynomial " I can't factor it out please help

$\displaystyle \left\{\dfrac{3x}{(2x - 1)} + 8\right\} = \dfrac{3x}{2x - 1} + \dfrac{8}{1}.$

How do you add fractions?

 

[manngaurav]

$\displaystyle \left\{\dfrac{3x}{(2x - 1)} + 8\right\} = \dfrac{3x}{2x - 1} + \dfrac{8}{1}.$

How do you add fractions?

hey there,
to add $\displaystyle \left\{\dfrac{3x}{(2x - 1)} + 8\right\} = \dfrac{3x}{2x - 1} + \dfrac{8}{1}.$
you multiply the denominator of first part with the numerator of second part and the denominator of the second part by the numerator of first part, and then divide the whole expression by the product of the denominators that is
$\displaystyle \left\{\dfrac{3x}{(2x - 1)} + \dfrac{8}{1}\right\} = \dfrac{3x(1) + 8(2x-1)}{(2x - 1)(1)}.$

hope it helped , and yes it is a polynomial , a polynomial is defined as axⁿ + bx + c where n can be any whole numbers that are 0,1,2,3.....n, , the highest power of x is known as the degree of polynomial as in this case there are two powers of x that are :1 and n, assuming n>1 then the given polynomial is said to be of degree n .

 

[Maddy_Math]

You must have grouping symbols around those certain exponents.

sorry I forgot those () around exponents thanks

 

[Maddy_Math]

hey there,
to add $\displaystyle \left\{\dfrac{3x}{(2x - 1)} + 8\right\} = \dfrac{3x}{2x - 1} + \dfrac{8}{1}.$
you multiply the denominator of first part with the numerator of second part and the denominator of the second part by the numerator of first part, and then divide the whole expression by the product of the denominators that is
$\displaystyle \left\{\dfrac{3x}{(2x - 1)} + \dfrac{8}{1}\right\} = \dfrac{3x(1) + 8(2x-1)}{(2x - 1)(1)}.$

hope it helped , and yes it is a polynomial , a polynomial is defined as axⁿ + bx + c where n can be any whole numbers that are 0,1,2,3.....n, , the highest power of x is known as the degree of polynomial as in this case there are two powers of x that are :1 and n, assuming n>1 then the given polynomial is said to be of degree n .

I guess you can't simplify it and it's not a polynomial as the denominator is not resolved
and if we try to solve it using binomial series then it will assume a negative exponent and won't stay a polynomial as polynomials can't have negative powers of variables

 

[manngaurav]

I guess you can't simplify it and it's not a polynomial as the denominator is not resolved
and if we try to solve it using binomial series then it will assume a negative exponent and won't stay a polynomial as polynomials can't have negative powers of variables

How can you simplify it more ..? if by simplifying you mean that solving for x then yes it is definitely possible, i think the whole thing cant be called polynomial rather it is a polynomial function

 

[DrPhil]

How can you simplify it more ..? if by simplifying you mean that solving for x then yes it is definitely possible, i think the whole thing cant be called polynomial rather it is a polynomial function

The ratio of two polynomials is called a "rational expression." From what I last saw posted, the numerator can still be simplified by combining like terms:

$\displaystyle \dfrac{19x - 8}{2x - 1}$